# Fractional Telegrapher’s Equation under Resetting: Non-Equilibrium Stationary States and First-Passage Times

## TL;DR

This paper studies a fractional telegraph equation with resetting, revealing non-equilibrium states and optimal resetting rates for first-passage times.

## Contribution

The paper introduces a novel approach to analyze fractional telegraph processes under resetting, revealing non-equilibrium stationary states and optimal resetting rates.

## Key findings

- The system reaches non-equilibrium stationary states in the long-time limit due to resetting.
- The mean squared displacement saturates as a result of the resetting mechanism.
- An optimal resetting rate minimizes the mean first-passage time.

## Abstract

We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal.